Glossary
Association
Two variables are associated if the conditional relative frequencies for one variable differ across the categories of the other variable. This means knowing the category of one variable helps predict the distribution of the other.
Example:
If the proportion of students who get good grades is much higher for those who attend tutoring sessions compared to those who don't, then there is an association between attending tutoring and getting good grades.
Bivariate variable
A statistical concept that refers to the relationship or analysis involving two variables, often used to describe the association between two categorical variables.
Example:
When investigating if there's a connection between a person's preferred coffee type (e.g., latte, espresso) and their age group, you are analyzing a bivariate variable relationship.
Categorical variable
A variable that places individuals into one of several groups or categories, without any inherent order or numerical meaning.
Example:
A student's favorite subject (e.g., Math, English, History, Science) is a categorical variable because it assigns them to a group.
Conditional Relative Frequency
The proportion of observations that fall into a specific category, given that they are already in another specific category.
Example:
The conditional relative frequency of students who prefer online classes given that they are seniors tells us what proportion of seniors prefer online classes.
Independence
Two variables are independent if the conditional relative frequencies for one variable are the same across all categories of the other variable. Knowing the category of one variable does not change the distribution of the other.
Example:
If the proportion of students who prefer coffee is the same for both freshmen and seniors, then class year and coffee preference are likely independent.
Joint Relative Frequency
The proportion of observations that fall into a specific combination of categories for two variables.
Example:
In a survey about pet ownership, the joint relative frequency of people who own both a cat AND a dog might be 0.05, meaning 5% of all surveyed individuals own both types of pets.
Marginal Relative Frequency
The proportion of observations that fall into a specific category of one variable, regardless of the other categories.
Example:
If 70% of all students surveyed prefer online classes, then 0.70 is the marginal relative frequency for preferring online classes.
Mosaic plots
A graphical display that visualizes the relationship between two categorical variables, where the area of each rectangle is proportional to the joint relative frequency.
Example:
A mosaic plot could visually represent the relationship between a person's preferred mode of transportation (car, bike, public transit) and their city of residence, with the size of each tile indicating the proportion of people in that specific combination.
Quantitative variable
A variable that takes numerical values for which arithmetic operations such as adding and averaging make sense.
Example:
The number of hours a student spends studying per week is a quantitative variable because it can be measured numerically and averaged.
Segmented bar graphs
A graphical display that shows the distribution of a categorical variable within each group, where each bar represents a group and is divided into segments proportional to the categories.
Example:
A segmented bar graph could illustrate the breakdown of majors (e.g., STEM, Humanities, Business) within each college year (freshman, sophomore, junior, senior), with each year having its own stacked bar.
Side-by-side bar graphs
A graphical display used to compare the distributions of a categorical variable across different groups.
Example:
To compare the favorite ice cream flavors of children versus adults, you could use a side-by-side bar graph with bars for each flavor grouped by age category.
Two-way tables
A statistical table that displays the frequencies or relative frequencies of two categorical variables in a cross-tabulated format, with one variable defining rows and the other defining columns.
Example:
A two-way table might summarize survey data on student grade level (e.g., 9th, 10th, 11th, 12th) and their preferred extracurricular activity (e.g., sports, clubs, arts).